Steady Heat Transfer Research Articles

Numerical simulation of the drag and heat-transfer characteristics around and through a porous particle based on the lattice Boltzmann method

Porous particle flow is universal in nature and industry. However, in previous numerical simulations, porous particles have usually been assumed to be solid. It is necessary to study the flow and heat-transfer characteristics around porous particles because they are greatly different from those of impermeable particles. In this study, two-dimensional steady flow and heat transfer around and through a porous particle with a constant temperature placed in a cold fluid were numerically investigated. The effects of the Reynolds number (Re) and Darcy number (Da) on the flow and heat-transfer characteristics were investigated in detail. The investigated ranges of the parameters were 10≤Re≤40 and 10−6≤Da≤10−2. It is sophisticated to simulate porous particles with traditional simulation methods because of their complicated structure. Therefore, the lattice Boltzmann method was used to solve the generalized macroscopic governing equations because of its simplicity. The drag coefficient decreased with increasing Re or Da, but the decrease was not prominent in the range 10−6≤Da≤10−4. The heat-transfer efficiency of the front surface was much stronger than that of the rear surface. The heat-transfer efficiency between the particle and the fluid increased with increasing Re or Da. However, for 10−6≤Da≤10−4, the increase was not prominent and the heat-transfer enhancement ratio was slightly larger than one. Furthermore, the effect of Da became more prominent at larger Re. In addition, new correlations for the drag coefficient and surface-averaged Nusselt number were obtained based on the simulated results.

Analysis of Al2O3-Cu nanofluid flow behaviour over a permeable moving wedge with convective surface boundary conditions

This research examines the steady flow and heat transfer over a moving wedge in Al2O3-Cu/water nanofluid with convective boundary condition. The governing partial differential equations (PDEs) are converted into nonlinear ordinary differential equations (ODEs) using similarity variables and then numerically solved using the built-in Matlab function (bvp4c).The impacts of wedge parameter, Biot number parameter, nanoparticle volume fraction, suction parameter together with moving parameter are investigated and presented graphically. The numerical evidences exhibit the existence of non-unique solution only when the free stream and wedge moves in the opposing direction. The range of similarity solutions to existis found to be larger for hybrid nanofluid compared to nanofluid. Also, increasing values of wedge parameter and nanoparticle volume fraction can delay the boundary layer separation. To identify which solution is physically stable, we performed the stability analysis. The results indicate that the first solution is stable.

Application of a MEMS heat flux sensor to heat transfer research on an impinging diesel jet

To clarify the mechanisms of heat transfer on an engine wall is an important challenge because the heat loss on the wall is one of the dominant factors that limit the thermal efficiency. A thin-film resistance type heat flux sensor fabricated with Micro-Electro-Mechanical Systems (MEMS) technologies was applied to research on the heat transfer of an impinging diesel jet. The MEMS sensor had a high sensitivity and multiple measurement points with a scale comparable to the turbulence of in-cylinder flow for the investigation of local instantaneous heat transfer characteristics in engines. Measurements of wall temperature and heat flux were conducted in a constant volume chamber under the reference conditions of Engine Combustion Network (ENC) Spray A with variations in injection pressure. As a result, the maximum heat flux and heat transfer coefficient reached about 5 MW/m2 and 3 MW/(m2 K), respectively. The results were compared to those obtained with a commercially available thermocouple, and both sensors produced similar trends. In addition, fluid motion near the wall was estimated from the heat flux fluctuations using a cross-correlation analysis. The relationship between heat transfer and flow was investigated in a dimensionless number fashion, and it was compared to a semi-theoretical prediction that was based on a steady state laminar flow heat transfer model.

Thermal performance and entropy generation of single‐layer and double‐layer constructal Y‐shaped bionic microchannel heat sinks

A kind of Y-shaped bionic microchannel (YBMC) heat sink is proposed and designed based on bionic concept and constructal law. A discontinuous Galerkin finite element method is applied to solve incompressible steady laminar flow and heat transfer in microchannels, and an optimal design strategy for geometrical parameters of the double-layer microchannels with counterflow arrangement is adopted. Results reveal that the proposed YBMC configuration provides much better thermal performance and lower total pressure drop subject to the same mass flow rate when compared to microchannels with rectangular straight configuration. Yet the YBMC design offers a more uniform temperature distribution along the heated surface. By using the principle of entropy generation, the degree of irreversible loss of the Y-shaped bionic cases is much less than those of the rectangular case. The pressure rises at the bifurcations of the first-stage, and the second-stage is related to the restart of boundary layer, confirming that the YBMC exhibits high thermal performance.

Numerical Calculation of Two-dimensional Steady Counterflows and Heat Transfer in H-shaped Channel

Numerical Calculation of Two-dimensional Steady Counterflows and Heat Transfer in H-shaped Channel

Microscale flow and heat transfer between the rotor and the flank for rotary engine

This paper is to investigate microscale flow and transfer between the rotor and the flank for rotary engine. The rotor and flank are simplified to two disks in order to study flow field and temperature field conveniently. The paper takes analysis of steady laminar flow and heat transfer between two disks separated by a gas-filled gap due to machining tolerance. A 3-D multi-physical coupling model is used, involving velocity slip, temperature jump, rarefaction, and dissipation. A solution based on commercial code COMSOL is derived and the results are used to illustrate the effects to velocity field, temperature distribution, disks' torque, and Nusselt number based on the governing parameters. The paper also investigates the effects of different modified Knudsen number on flow field and temperature field.

Wall reabsorption effects on heat and mass transfer of viscous fluid in a narrow leaky tube

The steady heat and mass transfer problem of flow of an incompressible Newtonian fluid is investigated in this study. The axisymmetric flow of a non-isothermal and highly viscous fluid is considered through a narrow leaky tube of uniform cross-section with linear reabsorption across the wall. The Navier–Stokes equations are solved for axially symmetric and slow flow in the tube. The effects of linear reabsorption parameter on the dimensionless radial and axial velocities, temperature, concentration, shear stress, leakage flux, fractional reabsorption, pressure drop across the tube as well as the Nusselt and Sherwood numbers have been investigated analytically. For 50% fractional reabsorption, inlet radial velocity is half of the reabsorption velocity along the tube. It has been shown that increase in the strength of linear reabsorption parameter considerably reduces the radial velocity, while, axial velocity shows opposite behaviour. At the exit region (z=0.9), reverse flow phenomenon is observed for higher values of reabsorption parameter. The pressure, flow rate and wall shear stress decreases after entrance region (z=0.1) of the tube. Nusselt number and Sherwood number show opposite behaviour inside the tube. At z=0.1 the magnitude of Nusselt number is maximum, while the Sherwood number is minimum at the exit region with higher value of reabsorption parameter.

Application of Capillary Network Air Conditioning System Based on Three-constant Technology in Gymnasium

With the advancement of social development, the continuous improvement of the level of science and technology puts higher requirements on the environmental quality of modern large-scale venues, which requires innovative concepts and high-tech to meet the requirements. In the paper, the capillary radiant air conditioning system based on three-constant technology is taken as the research object, and the steady heat transfer mathematical model of heat transfer from the cold water in the capillary network to the room is established. The structural parameters and operating parameters of the capillary radiant air conditioner are simulated and analyzed for the influence of its thermal performance, the environmental quality detection and control method based on bilinear model was established, and the algorithm of each index parameter was optimized to improve the high consistency between the model prediction parameters and the control tracking parameters. After verifying and testing the model parameters, it proves that the research content of the paper is real and effective, which its effect has reached the value of practical application. Through the research on the capillary network air conditioning system based on three-constant technology, it proves that the application in the construction of large venues has the effect of energy saving and environmental protection, and provides an innovative reference for the construction and development of the stadium.

Measurement of mid-low order of magnitude of heat transfer rate using infrared thermography in rarefied flow

Based on the analysis of demand for measuring heat transfer of hypersonic vehicle at high attitude, aimed at the characteristic of mid-low order of magnitude of heat transfer rate at ground test for simulating rarefied flow, various factors of the influence on measurement accuracy of mid-low order of magnitude of heat transfer were analyzed. Firstly, the influence of model heating time on heat transfer measurement was analyzed from reducing lateral error of experiment model to controlling temperature rise of model surface, which was based on a steady heat transfer of model surface and one-dimensional and semi-infinite hypothesis. Secondly, model adiabat materials with low thermal diffusivity were put to use. Transient Plane Source Method was introduced so as to calibrate thermal physical parameter(density, specific heat ratio and thermal conductivity) of model material with high accuracy. Kinds of method, such as diffusing compensation and phase-locked method, were adopted to raise measurement accuracy of model surface emittance. Finally, when using thin-wall calorimetry to obtain model surface heat transfer rate, thermocouple was welded on the inner surface of test model to measure heat transfer rate such as MW/m2 order of magnitude, while one was done on the outer surface of model to measure that with several kW/m2 to several hundred kW/m2 by thermocouple or by infrared thermography. In order to compare these results, on the experimental condition of Mach number 12, total pressure 4.2 MPa and total temperature 700 K, heat transfer rate at different points of the double cone thin-wall model was measured by thermocouple and infrared thermography simultaneously. The results indicated that the heat transfer rate measured with infrared thermometry was approaching to that done with thermocouple on the outer surface of model, that heat transfer rate by thermocouple on the outer surface of model was greater than that by thermocouple on the inner surface of test model, and that the influence of model heating time on the measurement of heat transfer rate with different order of magnitude was different.

Heat transfer in steady slip flow of tangent hyperbolic fluid over the lubricated surface of a stretchable rotatory disk

The heat transfer phenomenon is beneficial and applicable in engineering, industries, and technological processes. The production of energy with the help of some cheap resources plays a pivotal and renewable role in the industrial development of the countries. Owing to such a significant performance of heat transfer, the steady slip flow and heat transfer of tangent hyperbolic fluid over a lubricating surface of the stretchable rotatory disk is investigated. The effects of MHD, nonlinear radiation, and non-uniform heat source/sink subject to nonlinear boundary conditions are included in motion and energy equations. Because of the lubrication, a thin layer of the power-law fluid is produced at the surface of the disk. Since the lubricating layer is thin, the interfacial conditions are applied at the surface between the fluid and lubricant. The governing nonlinear partial differential equations (PDEs) have been converted into ordinary differential equations (ODEs), which are solved numerically using the Keller-box method. The upshots of pertinent parameters upon the dimensionless distributions of velocity and temperature are deliberated. The surface drag forces and heat transfer rates are computed, and the effects of governing parameters on them are examined. With the enhancement in the slip at the interface and Weissenberg number, the radial and azimuthal velocities enhances close to the disk, whereas they observe two diverse trends for the power-law index. Also, temperature escalates for radiation parameter, and this escalation is prominent for nonlinear radiation.

OVERLAPPING MULTI-DOMAIN SPECTRAL METHOD FOR NON-DARCIAN MIXED CONVECTION CHEMICALLY REACTING FLOW OF MICROPOLAR FLUID OVER A FLAT PLATE IN A POROUS MEDIA

An efficient overlapping multi-domain spectral method is presented and used in the analysis of a two-dimensional steady laminar MHD mixed convection flow, heat and mass transfer over a vertical flat plate embedded in a porous medium. The effect of chemical reaction, thermal radiation, heat source/sink and other parameters influencing the flow has been analyzed by imposing magnetic force transverse to the plate in a non-Darcy porous medium with constant wall temperature and concentration conditions. The flow equations are expressed in dimensionless form and solved using overlapping multidomain bivariate spectral local linearization method (OMD-BSLLM). An analysis of the convergence and accuracy of the OMD-BSLLM is given using error norms and residual errors. Comparisons with previously published work for special cases of the problem are performed and excellent concurrence is found; hence reliable results are being presented. The influence of certain parameters on the fluid properties and flow characteristics is analyzed. The skin friction, heat and mass transfer coefficients are presented for the concentrated flow and the turbulent boundary layer flow. The flow characteristics are found to be smaller for turbulent boundary layer flows than concentrated particle flows. This type of flow has an application in catalytic and chromatographic reactions, packed absorption and distillation towers.

Mixed convection flows of tangent hyperbolic fluid past an isothermal wedge with entropy: A mathematical study

AbstractThe nonlinear, steady, and mixed convective boundary layer flow and heat transfer of an incompressible tangent hyperbolic non‐Newtonian fluid over an isothermal wedge in the presence of magnetic field are analyzed numerically using the implicit Keller‐Box finite‐difference technique. The entropy analysis due to MHD flow of a tangent hyperbolic fluid past an isothermal wedge and viscous dissipation is also included. The numerical code is validated with previous Newtonian studies available in the literature. Graphical and tabulated results are analyzed to study the behavior of the fluid velocity, temperature, concentration, shear stress, heat transfer rate, entropy generation number, and Bejan number for various emerging thermophysical parameters, namely Weissenberg number (We), power‐law index (n), mixed convection parameter (λ), pressure gradient parameter (m), Prandtl number (Pr), Biot number (γ), Hartmann number (Ha), Brinkmann number (Br), Reynolds number (Re), and temperature gradient (Π). It is observed that velocity, entropy, Bejan number, and surface heat transfer rate are reduced with the increase in the Weissenberg number, but temperature and local skin friction are increased. An increase in pressure gradient enhances velocity, entropy, local skin friction, and surface heat transfer rate, but reduces temperature and Bejan number. An increase in an isothermal power‐law index (n) is observed to increase velocity, Bejan number, and surface heat transfer rate, but it decreases temperature, entropy, and local skin friction. An increase in the magnetic parameter (Ha) is found to decrease temperature, entropy, surface heat transfer rate, and local skin friction, and it increases velocity and Bejan number. The research is applicable for coating materials in chemical engineering, for instance, robust paints, production of aerosol deposition, and water‐soluble solution thermal treatment.

NUMERICAL INVESTIGATION OF THE MAGNETIC FIELD EFFECTS ON NATURAL CONVECTION WITHIN A POROUS HORIZONTAL CYLINDRICAL ANNULUS

A numerical study is performed to investigate the magnetic field effects on steady laminar natural convection heat transfer between two concentric horizontal cylinders filled with a porous medium. The inner cylinder surface is maintained at a hot temperature (Th), while the outer cylinder surface is at a cold temperature (Tc). The external magnetic field is applied parallel to the gravity. A non-Darcian model is used to simulate the flow in the porous medium. The governing equations in a body-fitted coordinate system were solved numerically using the finite difference method. Numerical results have covered a wide range of the modified Rayleigh number (25 ≤ Ra* ≤ 800) and the Hartmann number (0 ≤ Ha ≤ 10). The porosity of porous medium, Prandtl number, and Darcy number were taken as, 0.8, 0.7, and 3.2 × 10-6, respectively. The obtained results are depicted in terms of the streamlines, isotherms, and local and average Nusselt numbers, which show significant effects of Hartmann number and modified Rayleigh number on the fluid flow and temperature distribution inside the annulus. Also, it was found that the increase of magnetic field cause a reduction in the average Nusselt number, which leads to increasing in the thermal insulation.

Study on solving performance of VOSET + IDEAL with different algebraic equation solution methods

A method that combines VOSET and IDEAL was previously presented by the present authors for computing incompressible two-phase flow and heat transfer problems. The technique could provide an accurate calculation of a high-resolution phase interface. However, this method still has a considerable computational burden for complex transient two-phase flow and heat transfer problems. Therefore, to further optimize VOSET + IDEAL, the effects of five different algebraic equation solution methods (G-S point iteration, ADI, SIP, Bi-CGSTAB, and BCT-Bi-CGSTAB) on the solving performance of VOSET + IDEAL are analyzed using three typical two-phase examples. It can be concluded that: (1) the convergence rate of VOSET + IDEAL could be sped up as the efficiency of the algebraic equation solution methods improves, which is very different from the steady flow and heat transfer problems; (2) BCT-Bi-CGSTAB is the most efficient way among the five algebraic equation solution methods for increasing the convergence rate of VOSET + IDEAL. The research results can guide developing a more efficient way of simulating two-phase flows.

A theoretical analysis of steady three-dimensional flow and heat transfer of Power-Law nanofluid over a stretchable rotating disk filled with gyrotactic microorganisms

The current research study investigates the steady three-dimensional flow and heat transfer of a power-law nanofluid in the presence of the uniformly applied magnetic field and nonlinear thermal radiation over the stretchable rotating disk filled with gyrotactic microorganisms. The physically modeled partial differential equations (PDEs) are lessened to combined nonlinear ordinary differential equations (ODEs) with appropriate transformation. The influence of several types of pertinent parameters upon the dimensionless distributions of velocity, temperature, the concentration of nanoparticles, and microorganisms are analyzed graphically by solving the ODEs with a well-known shooting method. The tabular comparison is provided for the verification between the present results with those in the literature. Also, the physical quantities of interest are calculated, and the effects are scrutinized. Furthermore, it is noticed that the emerging parameters have produced a significant influence upon the velocity components, temperature, concentration of nanoparticles, and motile density of microorganisms.

Heat Transfer in Horizontal Copper Tube Heated by Electric Heating Process

Heat transfer from electrical and electronics component is essential for better performance of that electrical system, The maximum heat transfer from that system results long period durability. In most of the system base provided for equipments are very small and placed in a very complicated position. so heat transfer by forced convection is not easy for that purpose.The heat transfer by natural convection is the familiar technique used in electronics cooling; there is huge group of apparatus that lends itself to natural convection .This category consist of stand-alone correspondence such as modems and small computers having an array of printed circuit boards (PCB) accumulate within an area. Natural convection heat transfer in heated horizontal duct drive away heat from the interior surface is offered. The duct is open-ended and round in cross section. The test section is heated by provision of heating coils, where constant wall heat flux mentioned. Heat transfer experiment is carried out for channel of 50 mm. internal diameter and 4 mm thickness with length 600 mm. Ratios of length to diameter of the channel are taken as L/D = 12. Wall heat fluxes maintained at q// = 300 W/m2 to 3150 W/m2 . A methodical investigational record for the localsteady state natural convection heat transfer activities is obtained. The wall heating condition on local steady-state heat transfer phenomena are studied.The present experimental data is compared with the existing theoretical and experimental results for the cases of vertical smooth tubes.

Steady natural convection heat and mass transfer flow through a vertical porous channel with variable viscosity and thermal conductivity

AbstractThe present article studies the effects of suction/injection and variable physical properties on steady natural convection flow through a vertical channel. The investigation was done analytically using Differential Transformation Method (DTM). The variability in viscosity and thermal conductivity are considered linear function of temperature. The governing equations are transformed into a set of coupled nonlinear ordinary differential equations. Results obtained were compared with exact solution when some of the flow conditions were relaxed and results from DTM show an excellent agreement with the exact solution which was obtained analytically. The influence of the flow parameters on fluid temperature, concentration, and velocity are presented graphically and discussed for variations of the governing parameters. From the course of investigation, it was found that an increase in suction (S > 0) through the heated plate causes fluid temperature, velocity as well as concentration to decrease. However, an increase in injection causes heat transfer rate as well as skin friction at the heated plate to decrease.

Computation of radiative Marangoni (thermocapillary) magnetohydrodynamic convection in a Cu‐water based nanofluid flow from a disk in porous media: Smart coating simulation

AbstractWith emerging applications for smart and intelligent coating systems in energy, there has been increasing activity in researching magnetic nanomaterial coating flows. Surface tension features significantly in such regimes, and in the presence of heat transfer, Marangoni (thermocapillary) convection arises. Motivated by elaborating deeper the intrinsic transport phenomena in such systems, in this paper, a mathematical model is developed for steady radiative heat transfer and Marangoni magnetohydrodynamic flow of a Cu‐water nanofluid influencing a strong magnetic field through a porous disk. The semianalytical adomain decomposition method is employed to find the solution of flow governing equations, which are reduced into ordinary differential equation form via the Von Karman similarity transformation. Validation with a generalized differential quadrature algorithm is included. The response in dimensionless velocity, temperature, wall heat transfer rate and shear stress is investigated for various values of the control parameters. Temperature is reduced with increasing Marangoni parameter, whereas the flow is accelerated. With increasing permeability parameter, the temperatures are elevated. Increasing radiative flux boosts temperatures further from the disk surface. Increasing magnetic parameter strongly dampens the boundary layer flow and elevates the temperatures, also eliminating temperature oscillations at lower magnetic field strengths.

Steady flow and heat transfer of the power-law fluid between two stretchable rotating disks with non-uniform heat source/sink

This study aims to analyze the heat transfer phenomenon of power-law fluid with the occurrence of non-uniform heat source/sink within two stretchable disks which are parted with the constant distance and are co-axially rotating. The thermal conductivity is obeying the similar properties of power-law as that of viscosity. Von Karman’s generalized similarity transformation has been used firstly to reduce the physically modeled partial differential equations to nonlinear coupled ordinary differential equations and then tackled numerically with shooting method by finding missing initial conditions with the help of Newton–Raphson method and then system of equations are handled by means of RK-method. The influence of physical parameters for instance rotation as well as stretching, power-law index, Prandtl number, heat sink/source parameters upon non-dimensional velocity and temperature profiles are studied profoundly, later on, comprehensive analysis is expressed in discussion and results segment. The results which are computed numerically illustrate that the emerging parameters have substantial influences on velocity and temperature fields. In addition, rotation enhances the velocity components but temperature is predicting two diverse behaviors for shear-thinning and shear-thickening fluids, whenever upper and lower disk stretching it leads to an upsurge in radial and axial velocities but causes a decline in tangential velocity and temperature. Moreover, velocity and temperature distributions are in increasing trend except for the tangential component of the velocity which is decreasing by boosting the index of power-law. Furthermore, temperature decreases along with the similarity variable with the increasing Prandtl number but enhances with the enhancement in heat source/sink parameters. Finally, the skin friction in radial direction and local Nusselt number are escalating along the stretching parameters and Prandtl number but skin friction in tangential direction plummeting.

Suction Effect on Stagnation Point Flow and Heat Transfer over an Exponentially Shrinking Sheet in a Porous Medium

An investigation has been conducted to study the steady stagnation point flow and heat transfer in a porous medium caused by an exponentially stretching/shrinking sheet. Using a similarity transformation, the governing system of partial differential equations are transformed into a system of ordinary differential equations. The system of ordinary differential equations is then solved numerically using a shooting method in Maple software. The effect of the governing parameters on the skin friction coefficients and the local Nusselt numbers as well as the velocity and temperature profiles are analysed and discussed. Results obtain in this study are illustrated graphically. The range of parameter ???? where the similarity solution exists for the steady stagnation point over an exponentially shrinking sheet in porous medium is larger than linear shrinking sheet.